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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2508.07019 |
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| _version_ | 1866912530488623104 |
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| author | Vilches, Nicolás |
| author_facet | Vilches, Nicolás |
| contents | We study Bridgeland stability conditions on smooth surfaces arising from birational morphisms $S \to T$ to a singular surface. Assuming that $T$ has only ADE singularities or certain cyclic quotient singularities, we produce pre-stability conditions on $S$ whose central charges depend on the pullback of an ample divisor on $T$. Moreover, we prove the support property for the cyclic quotient case (including the $A_n$ singularities). These stability conditions arise as limits of the Arcara-Bertram stability conditions on $S$.
In a complementary direction, we study birational maps $S \to T$ for which a stability condition $S$ can be obtained using the pullback of an ample class on $T$. We prove that the morphism cannot contract smooth curves of positive genus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07019 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability conditions on surfaces and contractions of curves Vilches, Nicolás Algebraic Geometry 14F08, 18G80 We study Bridgeland stability conditions on smooth surfaces arising from birational morphisms $S \to T$ to a singular surface. Assuming that $T$ has only ADE singularities or certain cyclic quotient singularities, we produce pre-stability conditions on $S$ whose central charges depend on the pullback of an ample divisor on $T$. Moreover, we prove the support property for the cyclic quotient case (including the $A_n$ singularities). These stability conditions arise as limits of the Arcara-Bertram stability conditions on $S$. In a complementary direction, we study birational maps $S \to T$ for which a stability condition $S$ can be obtained using the pullback of an ample class on $T$. We prove that the morphism cannot contract smooth curves of positive genus. |
| title | Stability conditions on surfaces and contractions of curves |
| topic | Algebraic Geometry 14F08, 18G80 |
| url | https://arxiv.org/abs/2508.07019 |